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latex:feynman [2018/01/09 10:11] – [Gluon fusion] iwnlatex:feynman [2023/06/06 18:12] – iwn
Line 11: Line 11:
   * [[https://twiki.cern.ch/twiki/bin/viewauth/CMS/SUSYSimplifiedModelDiagrams|ready-made SUSY diagrams (images)]], with the [[https://github.com/CMS-SUS-XPAG/SUSYDiagrams|code (GitHub)]];   * [[https://twiki.cern.ch/twiki/bin/viewauth/CMS/SUSYSimplifiedModelDiagrams|ready-made SUSY diagrams (images)]], with the [[https://github.com/CMS-SUS-XPAG/SUSYDiagrams|code (GitHub)]];
   * [[http://osksn2.hep.sci.osaka-u.ac.jp/~taku/osx/feynmp_latexit.html|how to set up feynMP in LaTeXiT on Mac OS X]] to make Feynman diagrams as standalone images (strongly recommended);   * [[http://osksn2.hep.sci.osaka-u.ac.jp/~taku/osx/feynmp_latexit.html|how to set up feynMP in LaTeXiT on Mac OS X]] to make Feynman diagrams as standalone images (strongly recommended);
 +  * [[https://www.overleaf.com/learn/latex/Feynman_diagrams#Other_packages_for_drawing_Feynman_diagrams|Excelent tutorial by Overleaf]];
   * [[latex:feynman_file|macro for typesetting Feynman graphs in a LaTeX file]];   * [[latex:feynman_file|macro for typesetting Feynman graphs in a LaTeX file]];
-  * [[latex:feynman_equation_file|using Feynman diagrams in equation in a LaTeX text]]. +  * [[latex:feynman_equation_file|using Feynman diagrams in equation in a LaTeX text]]; 
- +  * [[latex:tikz|more general TikZ diagrams]].
  
  ===== Simple example: electron - muon scattering =====  ===== Simple example: electron - muon scattering =====
Line 62: Line 62:
 Checkout the [[http://www.pd.infn.it/TeX/doc/latex/feynmf/manual.pdf|feynMF manual]] for all the available line styles, line options, vertex options and all their parameters. Checkout the [[http://www.pd.infn.it/TeX/doc/latex/feynmf/manual.pdf|feynMF manual]] for all the available line styles, line options, vertex options and all their parameters.
  
-<WRAP group><WRAP half column 55% centeralign>+<WRAP group><WRAP half column 60% centeralign>
 **Table 1**: Available line styles  of ''\fmf''. **Table 1**: Available line styles  of ''\fmf''.
-{{ latex:fmfmp_line_styles_table.png ? 420 }}+{{ latex:fmfmp_line_styles_table.png ? 500 }}
 </WRAP><WRAP half column 37% centeralign > </WRAP><WRAP half column 37% centeralign >
-**Table 2**: Available line options of ''\fmf''. +**Table 2**: Available line styles  of ''\fmf''. 
-{{ latex:fmfmp_line_options_table.png ? 270 }}+{{ latex:fmfmp_line_styles_table2.png ? 600 }}
 \\ \\
-**Table 3**: Available vertex options of ''\fmfv''. +**Table 3**: Available line options of ''\fmf''. 
-{{ latex:fmfmp_vertex_options_table.png ? 300 }}+{{ latex:fmfmp_line_options_table.png ? 600 }} 
 +\\ 
 +**Table 4**: Available vertex options of ''\fmfv''. 
 +{{ latex:fmfmp_vertex_options_table.png ? 600 }}
 </WRAP></WRAP> </WRAP></WRAP>
  
Line 298: Line 301:
 \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
-\\ \\ 
  
  
  
 + ===== Bent lines and loop ===== 
  
 +Lines can be bent by simply adding ''right'' or ''left''. Here is for example the one-loop correction to the electron-photon vertex to compute the anomalous magnetic momentum:
 +
 +<WRAP group><WRAP half column lo 55%>
 +<code latex>
 +\LARGE
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(70,100)
 +    \fmfleft{f2,f1}
 +    \fmfright{p} % outgoing photon
 +    \fmf{boson,l.s=left,t=0.8}{p,v}
 +    \fmf{fermion}{f2,v1}
 +    \fmf{plain,t=1.5}{v1,v,v2}
 +    \fmf{fermion}{v2,f1}
 +    \fmfv{l.a=165,l=e$^-$}{f1} % outcoming electron
 +    \fmfv{l.a=-165,l=e$^-$}{f2} % incoming electron
 +    \fmffreeze
 +    \fmf{boson,left}{v1,v2} % bend photon line to the left
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column lo 40%>
 +{{ latex:feynman:electron_vertex_loop.png ? 210 }}
 +</WRAP></WRAP>
 +
 +More examples can be found below in the sections on [[#higgs_mass_loop_corrections_with_susy_and_vlqs|Higgs mass corrections]] and [[#penguin_diagrams|Penguin diagrams]].
 +\\ \\
  ====== Intermediate mode: How to use MetaPost ======  ====== Intermediate mode: How to use MetaPost ======
  
Line 505: Line 534:
  
 Some Feynman diagrams contributing to top quark pair production via gluon-gluon fusion: Some Feynman diagrams contributing to top quark pair production via gluon-gluon fusion:
 +
 +Full code for a {{latex:feynman:ttbar.pdf|multipage PDF}} including all figures below can be found [[latex:feynman:ttbar|here]].
  
 <WRAP group><WRAP half column lo> <WRAP group><WRAP half column lo>
Line 512: Line 543:
     \fmfleft{i2,i1}     \fmfleft{i2,i1}
     \fmfright{o2,o1}     \fmfright{o2,o1}
 +    % main
 +    \fmf{fermion}{i1,v1,i2}
     \fmf{fermion}{o2,v2,o1}     \fmf{fermion}{o2,v2,o1}
-    \fmf{gluon}{i2,v1,i1} +    \fmf{gluon,label=$g$,label.side=right,label.dist=10}{v2,v1} 
-    \fmf{gluon,label=$g$}{v1,v2} +    % labels 
-    \fmflabel{$g$}{i1} +    \fmflabel{$q$}{i1} 
-    \fmflabel{$g$}{i2} +    \fmflabel{$\overline{q}$}{i2} 
-    \fmflabel{$\bar{t}$}{o2} +    \fmflabel{$\overline{\text{t}}$}{o2} 
-    \fmflabel{$t$}{o1}+    \fmflabel{t}{o1}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 524: Line 557:
 </WRAP><WRAP half column> </WRAP><WRAP half column>
 \\ \\
-{{ latex:ggttbar1.png ? 220 }}+{{ latex:feynman:qqttbar.png ? 220 }}
 \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
Line 532: Line 565:
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
   \begin{fmfgraph*}(110,60)   \begin{fmfgraph*}(110,60)
-    \fmfleft{i2,i1}  +    \fmfleft{i2,i1} 
-    \fmfright{o2,o1}  +    \fmfright{o2,o1} 
-    \fmf{gluon}{v1,i1}  +    \fmfshift{2 left}{i1} 
-    \fmf{fermion}{v1,o1} +    \fmf{fermion}{o2,v2,o1} 
-    \fmf{gluon}{i2,v2} +    \fmf{gluon}{v1,i1} 
-    \fmf{fermion}{o2,v2} +    \fmf{gluon}{v1,i2} 
-    \fmf{fermion, label=$t$}{v2,v1} +    \fmf{gluon,label=$g$}{v1,v2} 
-    \fmflabel{$g$}{i2} +    % labels 
-    \fmflabel{$g$}{i1} +    \fmfv{l.d=4,l=$g$}{i1} 
-    \fmflabel{$t$}{o1} +    \fmfv{l.d=6,l=$g$}{i2} 
-    \fmflabel{$\bar{t}$}{o2}+    \fmflabel{$\overline{\text{t}}$}{o2} 
 +    \fmflabel{t}{o1}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 548: Line 582:
 </WRAP><WRAP half column> </WRAP><WRAP half column>
 \\ \\
-{{ latex:ggttbar2.png ? 220 }}+{{ latex:feynman:ggttbar1.png ? 220 }}
 \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
Line 558: Line 592:
     \fmfleft{i2,i1}     \fmfleft{i2,i1}
     \fmfright{o2,o1}     \fmfright{o2,o1}
-    \fmf{fermion}{i1,v1,i2} +    % main 
-    \fmf{fermion}{o2,v2,o1} +    \fmf{gluon}{v1,i1} 
-    \fmf{gluon,label=$g$,label.side=right,label.dist=10}{v2,v1} +    \fmf{fermion}{v1,o1} 
-    \fmflabel{$q$}{i1} +    \fmf{gluon}{i2,v2} 
-    \fmflabel{$\overline{q}$}{i2} +    \fmf{fermion}{o2,v2} 
-    \fmflabel{$\bar{t}$}{o2} +    \fmf{fermion,label=t}{v2,v1} 
-    \fmflabel{$t$}{o1}+    % labels 
 +    \fmflabel{$g$}{i2} 
 +    \fmflabel{$g$}{i1} 
 +    \fmfv{l.d=7,l.a=22,l=t}{o1} 
 +    \fmfv{l.d=7,l.a=-20,l=$\overline{\text{t}}$}{o2}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 570: Line 608:
 </WRAP><WRAP half column> </WRAP><WRAP half column>
 \\ \\
-{{ latex:qqttbar.png ? 220 }}+{{ latex:feynman:ggttbar3.png ? 220 }}
 \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
  
- +With radiated quarks or gluons that will form hard jets:
- +
-With jets:+
  
 <WRAP group><WRAP half column lo> <WRAP group><WRAP half column lo>
Line 582: Line 618:
 \large \large
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
-  \begin{fmfgraph*}(125,75)+  \begin{fmfgraph*}(120,70)
     \fmfleft{i2,i1}     \fmfleft{i2,i1}
     \fmfright{o2,o1}     \fmfright{o2,o1}
     \fmftop{t}     \fmftop{t}
 +    \fmfshift{5 up}{t}
 +    % skeleton
     \fmf{phantom}{i1,v1,i2}     \fmf{phantom}{i1,v1,i2}
     \fmf{phantom}{o1,v2,o2}     \fmf{phantom}{o1,v2,o2}
     \fmf{phantom}{v1,v2}     \fmf{phantom}{v1,v2}
     \fmffreeze     \fmffreeze
-    \fmfshift{5 left}{i1} +    % main 
-    \fmfshift{5 up}{i1,t} +    \fmf{fermion}{i1,g} 
-    \fmf{gluon,tension=0.8}{g,i1} +    \fmf{plain,tension=2.8}{g,v1} 
-    \fmf{fermion}{v1,g} +    \fmf{fermion}{v1,i2} 
-    \fmf{gluon}{v1,i2} +    \fmf{gluon,tension=0}{t,g}
-    \fmf{fermion,tension=0}{g,t}+
     \fmf{gluon}{v1,v2}     \fmf{gluon}{v1,v2}
     \fmf{fermion}{o2,v2,o1}     \fmf{fermion}{o2,v2,o1}
-    \fmflabel{$g$}{i1} +    % labels 
-    \fmflabel{$g$}{i2}+    \fmflabel{$q$}{i1} 
 +    \fmflabel{$\overline{q}$}{i2} 
 +    \fmfv{l.d=5,l.a=25,l=$g$}{t}
     \fmflabel{$\bar{\text{t}}$}{o2}     \fmflabel{$\bar{\text{t}}$}{o2}
     \fmflabel{$\text{t}$}{o1}     \fmflabel{$\text{t}$}{o1}
Line 607: Line 646:
 </WRAP><WRAP half column> </WRAP><WRAP half column>
 \\ \\ \\ \\
-{{ latex:ggttbar_quark.png ? 220 }}+{{ latex:feynman:qqttbar_gluon.png ? 220 }}
 \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
- 
  
  
Line 617: Line 655:
 \large \large
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
-  \begin{fmfgraph*}(125,75)+  \begin{fmfgraph*}(120,75)
     \fmfleft{i2,i1}     \fmfleft{i2,i1}
     \fmfright{o2,o1}     \fmfright{o2,o1}
     \fmftop{t}     \fmftop{t}
 +    \fmfshift{4 left}{i1}
 +    \fmfshift{2 left}{i2}
 +    \fmfshift{5 up}{t}
 +    % skeleton
     \fmf{phantom}{i1,v1,i2}     \fmf{phantom}{i1,v1,i2}
     \fmf{phantom}{o1,v2,o2}     \fmf{phantom}{o1,v2,o2}
-    \fmf{phantom}{v1,v2}+    \fmf{phantom,tension=1.2}{v1,v2}
     \fmffreeze     \fmffreeze
-    %\fmfshift{5 left}{i1} +    % main
-    %\fmfshift{5 up}{i1,t}+
     \fmf{gluon,tension=0.8}{g,i1}     \fmf{gluon,tension=0.8}{g,i1}
     \fmf{fermion}{v1,g}     \fmf{fermion}{v1,g}
-    \fmf{fermion}{i2,v1}+    \fmf{gluon}{v1,i2}
     \fmf{fermion,tension=0}{g,t}     \fmf{fermion,tension=0}{g,t}
     \fmf{gluon}{v1,v2}     \fmf{gluon}{v1,v2}
     \fmf{fermion}{o2,v2,o1}     \fmf{fermion}{o2,v2,o1}
-    \fmflabel{$g$}{i1} +    % labels 
-    \fmflabel{$q$}{i2}+    \fmfv{l.d=4,l=$g$}{i1} 
 +    \fmfv{l.d=6,l=$g$}{i2} 
 +    \fmfv{l.d=5,l.a=25,l=$q$}{t}
     \fmflabel{$\bar{\text{t}}$}{o2}     \fmflabel{$\bar{\text{t}}$}{o2}
     \fmflabel{$\text{t}$}{o1}     \fmflabel{$\text{t}$}{o1}
Line 642: Line 685:
 </WRAP><WRAP half column> </WRAP><WRAP half column>
 \\ \\ \\ \\
-{{ latex:gqttbar_quark.png ? 220 }}+{{ latex:feynman:ggttbar_quark.png ? 220 }}
 \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
Line 652: Line 695:
 \large \large
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
-  \begin{fmfgraph*}(120,70)+  \begin{fmfgraph*}(120,75)
     \fmfleft{i2,i1}     \fmfleft{i2,i1}
     \fmfright{o2,o1}     \fmfright{o2,o1}
     \fmftop{t}     \fmftop{t}
 +    \fmfshift{4 left}{i1}
 +    \fmfshift{2 left}{i2}
 +    \fmfshift{5 up}{t}
 +    % skeleton
     \fmf{phantom}{i1,v1,i2}     \fmf{phantom}{i1,v1,i2}
     \fmf{phantom}{o1,v2,o2}     \fmf{phantom}{o1,v2,o2}
-    \fmf{phantom}{v1,v2}+    \fmf{phantom,tension=1.2}{v1,v2}
     \fmffreeze     \fmffreeze
-    \fmf{fermion}{i1,g} +    % main 
-    \fmf{plain,tension=2.8}{g,v1} +    \fmf{gluon,tension=0.8}{g,i1} 
-    \fmf{fermion}{v1,i2} +    \fmf{fermion}{v1,g} 
-    \fmf{gluon,tension=0}{t,g}+    \fmf{fermion}{i2,v1} 
 +    \fmf{fermion,tension=0}{g,t}
     \fmf{gluon}{v1,v2}     \fmf{gluon}{v1,v2}
     \fmf{fermion}{o2,v2,o1}     \fmf{fermion}{o2,v2,o1}
-    \fmflabel{$q$}{i1} +    % labels 
-    \fmflabel{$\overline{q}$}{i2}+    \fmfv{l.d=4,l=$g$}{i1} 
 +    \fmfv{l.d=6,l=$q$}{i2} 
 +    \fmfv{l.d=5,l.a=25,l=$q$}{t}
     \fmflabel{$\bar{\text{t}}$}{o2}     \fmflabel{$\bar{\text{t}}$}{o2}
     \fmflabel{$\text{t}$}{o1}     \fmflabel{$\text{t}$}{o1}
Line 675: Line 725:
 </WRAP><WRAP half column> </WRAP><WRAP half column>
 \\ \\ \\ \\
-{{ latex:gqttbar_quark.png ? 220 }}+{{ latex:feynman:gqttbar_quark.png ? 220 }}
 \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
- 
  
  
Line 700: Line 749:
     \fmf{boson,label=$\text{Z}/\gamma^*$,label.side=right}{v1,v2}     \fmf{boson,label=$\text{Z}/\gamma^*$,label.side=right}{v1,v2}
     \fmflabel{$q$}{i1}     \fmflabel{$q$}{i1}
-    \fmflabel{$q'$}{i2} +    \fmflabel{$\overline{q}$}{i2} 
-    \fmflabel{$\bar{\ell}$}{o2} +    \fmflabel{$\ell^+$}{o2} 
-    \fmflabel{$\ell$}{o1}+    \fmflabel{$\ell^-$}{o1}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 737: Line 786:
     \fmflabel{$g$}{i1}     \fmflabel{$g$}{i1}
     \fmflabel{$q$}{i2}     \fmflabel{$q$}{i2}
-    \fmflabel{$q'$}{t} +    \fmfv{l.a=25,l=$q$}{t} 
-    \fmflabel{$\bar{\ell}$}{o2} +    \fmflabel{$\ell^+$}{o2} 
-    \fmflabel{$\ell$}{o1}+    \fmflabel{$\ell^-$}{o1}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 769: Line 818:
     \fmflabel{$q$}{i1}     \fmflabel{$q$}{i1}
     \fmflabel{$q'$}{i2}     \fmflabel{$q'$}{i2}
-    \fmflabel{$\bar{\ell}$}{o2} +    \fmflabel{$\ell^+$}{o2} 
-    \fmflabel{$\ell$}{o1}+    \fmflabel{$\ell^-$}{o1}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 1087: Line 1136:
 <WRAP group><WRAP half column lo> <WRAP group><WRAP half column lo>
 <code latex> <code latex>
 +\large
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
   \begin{fmfgraph*}(150,80)   \begin{fmfgraph*}(150,80)
Line 1111: Line 1161:
 <WRAP group><WRAP half column lo> <WRAP group><WRAP half column lo>
 <code latex> <code latex>
 +\large
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
-  \begin{fmfgraph*}(150,80)+  \begin{fmfgraph*}(150,90)
     \fmfleft{d,i1,d,d,i3,d}     \fmfleft{d,i1,d,d,i3,d}
     \fmfright{o1,d,o2,d,o3}     \fmfright{o1,d,o2,d,o3}
Line 1119: Line 1170:
     \fmf{phantom,tension=0.3}{v1,v3}     \fmf{phantom,tension=0.3}{v1,v3}
     \fmffreeze     \fmffreeze
-    \fmf{boson,label=$V$,label.side=left,tension=0.7}{v3,v2,v1}+    \fmf{boson,label=$V^*$,label.side=left,tension=0.7}{v3,v2,v1}
     \fmf{dashes}{v2,o2}     \fmf{dashes}{v2,o2}
     \fmflabel{$q$}{i3}     \fmflabel{$q$}{i3}
Line 1135: Line 1186:
 <WRAP group><WRAP half column lo> <WRAP group><WRAP half column lo>
 <code latex> <code latex>
 +\large
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
   \begin{fmfgraph*}(120,60)   \begin{fmfgraph*}(120,60)
Line 1157: Line 1209:
 \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
- 
  
  
Line 1246: Line 1297:
 <WRAP group><WRAP half column lo> <WRAP group><WRAP half column lo>
 <code latex> <code latex>
 +\large
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
   \begin{fmfgraph*}(170,60)   \begin{fmfgraph*}(170,60)
Line 1281: Line 1333:
 <WRAP group><WRAP half column lo> <WRAP group><WRAP half column lo>
 <code latex> <code latex>
 +\large
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
   \begin{fmfgraph*}(170,60)   \begin{fmfgraph*}(170,60)
Line 1309: Line 1362:
 \\ \\ \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
- 
  
  
Line 1318: Line 1370:
 <WRAP group><WRAP half column lo> <WRAP group><WRAP half column lo>
 <code latex> <code latex>
 +\large
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
   \begin{fmfgraph*}(140,90)   \begin{fmfgraph*}(140,90)
Line 1343: Line 1396:
 \\ \\ \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
- 
  
  
Line 1517: Line 1569:
     \fmflabel{$\tau^-$}{t1}     \fmflabel{$\tau^-$}{t1}
     \fmflabel{$\tau^+$}{t2}     \fmflabel{$\tau^+$}{t2}
-    \fmflabel{$b$}{b1}+    \fmflabel{b}{b1}
     \fmflabel{$\overline{\text{b}}$}{b2}     \fmflabel{$\overline{\text{b}}$}{b2}
   \end{fmfgraph*}   \end{fmfgraph*}
Line 1523: Line 1575:
 </code> </code>
 </WRAP><WRAP 40% column> </WRAP><WRAP 40% column>
-\\ 
 {{ latex:ggbbh_bbaa_bbtautau.png ? 280 }} {{ latex:ggbbh_bbaa_bbtautau.png ? 280 }}
-\\ \\ 
 </WRAP></WRAP> </WRAP></WRAP>
  
Line 1532: Line 1582:
 \large \large
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
-  \begin{fmfgraph*}(130,130) +  \begin{fmfgraph*}(180,140) 
-    \fmfleft{d,d,g2,d,g1,d,d} +    \fmfstraight 
-    \fmfright{b2,d,t2,d,t1,d,b1} +    \fmfleft{i2,g2,g1,i1} 
-    \fmf{gluon,tension=2}{v1,g1} +    \fmfright{o4,o3,o2,o1} 
-    \fmf{gluon,tension=2}{g2,v2} +    \fmftop{top} 
-    \fmf{phantom}{v1,t1} +    \fmfbottom{bot} 
-    \fmf{phantom}{v2,t2}+    % gluon 
 +    \fmf{gluon,tension=2.6}{t1,g1} 
 +    \fmf{gluon,tension=2.6}{g2,t2} 
 +    \fmf{phantom,tension=0.4}{o1,t1,o3} 
 +    \fmf{phantom,tension=0.4}{o2,t2,o4}
     \fmffreeze     \fmffreeze
-    \fmf{fermion}{b2,v2,v3,v1,b1} +    % top loop 
-    \fmf{dashes,tension=1.5,label=$a$,l.s=left}{v3,a} +    \fmf{fermion,tension=1.0}{t1,t3,t2,t1} 
-    \fmf{fermion}{t2,a,t1}+    \fmf{phantom,tension=0.4}{o3,t3,o2} 
 +    \fmffreeze 
 +    % Higgs bosons 
 +    \fmf{dashes,tension=1.4,label=H,l.s=left}{t3,h} 
 +    \fmf{dashes,tension=1.2,label=$a$,l.s=right}{v1,h,v2} 
 +    % decay products 
 +    \fmf{phantom,tension=0.8}{top,v1} 
 +    \fmf{phantom,tension=0.8}{v2,bot} 
 +    \fmfshift{16 down}{o1} 
 +    \fmfshift{ 8 down}{o2} 
 +    \fmfshift{ 8 up}{o3} 
 +    \fmfshift{16 up}{o4} 
 +    \fmf{fermion,tension=1.8}{o2,v1,o1} 
 +    \fmf{fermion,tension=1.8}{o4,v2,o3} 
 +    % labels
     \fmflabel{$g$}{g1}     \fmflabel{$g$}{g1}
     \fmflabel{$g$}{g2}     \fmflabel{$g$}{g2}
-    \fmflabel{$\tau^-$}{t1} +    \fmflabel{$\text{b}$}{o1} 
-    \fmflabel{$\tau^+$}{t2} +    \fmflabel{$\overline{\text{b}}$}{o2} 
-    \fmflabel{$b$}{b1} +    \fmflabel{$\tau^-$}{o3} 
-    \fmflabel{$\overline{\text{b}}$}{b2}+    \fmflabel{$\tau^+$}{o4}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 1597: Line 1665:
 \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
- 
- 
  ===== Leptoquark =====  ===== Leptoquark =====
  
 Here are some examples of processes with leptoquarks. Here are some examples of processes with leptoquarks.
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\LARGE
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(100,80)
 +    \fmfleft{LQ}
 +    \fmfright{q,l}
 +    \fmf{dashes,l.s=left,t=1.2}{LQ,v}
 +    \fmf{fermion}{v,q}
 +    \fmf{fermion}{v,l}
 +    \fmfv{l=LQ}{LQ}
 +    \fmfv{l.a=-28,l=$q$}{q}
 +    \fmfv{l.a=28,l=$\ell$}{l}
 +    \fmfdot{v}
 +    \fmfv{l.a=115,l=\large$\lambda_{\ell q}$}{v}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\
 +{{ latex:feynman:lq_coupling_lq.png ? 250 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +
 +
 + ==== Pair production ====
  
 <WRAP group><WRAP 55% column lo> <WRAP group><WRAP 55% column lo>
Line 1607: Line 1701:
 \large \large
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
-  \begin{fmfgraph*}(140,100) +  \begin{fmfgraph*}(120,120) 
-    \fmfleft{i2,i1} +    \fmfstraight 
-    \fmfright{o2,l2,l1} +    \fmfleft{i2,g2,d,g1,i1} 
-    % gluon + quarks +    \fmfright{o4,o3,o2,o1} 
-    \fmf{gluon}{i1,v1} +    \fmftop{top} 
-    \fmf{fermion}{i2,v2,o2} +    \fmfbottom{bot} 
-    \fmflabel{$g$}{i1} +    % gluonS 
-    \fmflabel{$q$}{i2} +    \fmf{gluon,tension=1.4}{v,g1} 
-    \fmflabel{$\ell$}{o2} +    \fmf{gluon,tension=1.4}{g2,v} 
-    % LQs +    \fmf{gluon,tension=1.6}{v,h} 
-    \fmf{dashes_arrow,label=LQ,label.side=left}{v2,v1,LQ} +    \fmf{dashes,tension=1.2,label=LQ,l.s=right}{v1,h} 
-    % LQ -> lepton + quark +    \fmf{dashes,tension=1.2,label=$\overline{\text{LQ}}$,l.s=right}{h,v2} 
-    \fmf{fermion}{l2,LQ,l1} +    % decay products 
-    \fmflabel{$q$}{l1} +    \fmf{phantom,tension=0.8}{top,v1} 
-    \fmflabel{$\overline{\ell}$}{l2}+    \fmf{phantom,tension=0.8}{v2,bot} 
 +    \fmfshift{16 down}{o1} 
 +    \fmfshift{ 8 down}{o2} 
 +    \fmfshift{ 8 up}{o3} 
 +    \fmfshift{16 up}{o4} 
 +    \fmf{fermion,tension=1.8}{o1,v1,o2} 
 +    \fmf{fermion,tension=1.8}{o4,v2,o3} 
 +    % labels 
 +    \fmflabel{$g$}{g1} 
 +    \fmflabel{$g$}{g2} 
 +    \fmflabel{$\overline{\ell}$}{o1} 
 +    \fmflabel{$q$}{o2} 
 +    \fmflabel{$\ell$}{o3} 
 +    \fmflabel{$\overline{q}$}{o4}
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
Line 1627: Line 1734:
 </WRAP><WRAP 40% column> </WRAP><WRAP 40% column>
 \\ \\ \\ \\
-{{ latex:lq_single_t-channel_llq.png ? 250 }}+{{ latex:feynman:lq_pair_qqll.png ? 400 }}
 \\ \\ \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
Line 1635: Line 1742:
 \large \large
 \begin{fmffile}{feyngraph} \begin{fmffile}{feyngraph}
-  \begin{fmfgraph*}(120,100)+  \begin{fmfgraph*}(100,120)
     \fmfstraight     \fmfstraight
-    \fmfleft{i2,i1} +    \fmfleft{i2,g,i1} 
-    \fmfright{o2,l2,l1} +    \fmfright{o4,o3,o2,o1} 
-    % skeleton +    \fmftop{top} 
-    \fmf{phantom,tension=1.8}{i1,v1} +    \fmfbottom{bot} 
-    \fmf{phantom,tension=1.0}{v1,l1} +    % gluonS 
-    \fmf{phantom,tension=1.8}{v1,v2} +    \fmf{gluon,tension=1.6}{g,h} 
-    \fmf{phantom,tension=1.8}{i2,v2} +    \fmf{dashes,tension=1.3,label=LQ,l.s=right}{v1,h} 
-    \fmf{phantom,tension=1.0}{v2,o2} +    \fmf{dashes,tension=1.3,label=$\overline{\text{LQ}}$,l.s=right}{h,v2} 
-    \fmffreeze +    % decay products 
-    % gluon + quarks +    \fmf{phantom,tension=1.0}{top,v1} 
-    \fmf{gluon}{i1,v1} +    \fmf{phantom,tension=1.0}{v2,bot} 
-    \fmf{fermion}{i2,v2,o2} +    \fmfshift{16 down}{o1} 
-    \fmflabel{$g$}{i1} +    \fmfshift{ 8 down}{o2} 
-    \fmflabel{$q$}{i2} +    \fmfshift{ 8 up}{o3} 
-    \fmflabel{$\ell$}{o2} +    \fmfshift{16 up}{o4} 
-    % LQs +    \fmf{fermion,tension=1.8}{o1,v1,o2} 
-    \fmf{dashes_arrow,tension=1.2,label=LQ,label.side=left}{v1,LQ} +    \fmf{fermion,tension=1.8}{o4,v2,o3} 
-    \fmf{dashes_arrow,label=LQ,label.side=left}{v2,v1} +    % labels 
-    % LQ -> lepton + quark +    \fmflabel{$g$}{g} 
-    \fmf{fermion}{l2,LQ,l1} +    \fmflabel{$\tau^+$}{o1} 
-    \fmfshift{5 right}{l1,l2} +    \fmflabel{b}{o2} 
-    \fmfshift{20 left}{o2} +    \fmflabel{\vspace{8pt}$\tau^-$}{o3} 
-    \fmflabel{$q$}{l1} +    \fmflabel{$\overline{\text{b}}$}{o4}
-    \fmflabel{$\overline{\ell}$}{l2}+
   \end{fmfgraph*}   \end{fmfgraph*}
 \end{fmffile} \end{fmffile}
 </code> </code>
 </WRAP><WRAP 40% column> </WRAP><WRAP 40% column>
-\\ \\ \\ \\ +\\ \\ 
-{{ latex:lq_single_t-channel_llq_straight.png ? 250 }} +{{ latex:feynman:lq_pair_bbtautau_short.png ? 250 }} 
-\\ \\ \\ \\ \\+\\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
 +
 +
 +
 + ==== Single production ====
  
 <WRAP group><WRAP 55% column lo> <WRAP group><WRAP 55% column lo>
Line 1686: Line 1796:
     \fmflabel{$\ell$}{o2}     \fmflabel{$\ell$}{o2}
     % LQ     % LQ
-    \fmf{dashes_arrow,label=LQ,label.side=left}{v2,LQ}+    \fmf{dashes,label=LQ,label.side=left}{v2,LQ}
     % LQ -> lepton + quark     % LQ -> lepton + quark
     \fmf{fermion}{l2,LQ,l1}     \fmf{fermion}{l2,LQ,l1}
Line 1697: Line 1807:
 </WRAP><WRAP 40% column> </WRAP><WRAP 40% column>
 \\ \\ \\ \\ \\ \\
-{{ latex:lq_single_s-channel_llq.png ? 250 }}+{{ latex:feynman:lq_single_qll_skewed.png ? 250 }}
 \\ \\ \\ \\ \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
Line 1731: Line 1841:
     \fmflabel{$\ell$}{l}     \fmflabel{$\ell$}{l}
     % LQ     % LQ
-    \fmf{dashes_arrow,tension=1.2,label=LQ,label.side=left}{v2,LQ}+    \fmf{dashes,tension=1.2,label=LQ,label.side=left}{v2,LQ}
     % LQ -> lepton + quark     % LQ -> lepton + quark
     \fmf{fermion}{l2,LQ,l1}     \fmf{fermion}{l2,LQ,l1}
Line 1742: Line 1852:
 </WRAP><WRAP 40% column> </WRAP><WRAP 40% column>
 \\ \\ \\ \\ \\ \\ \\ \\
-{{ latex:lq_single_s-channel_llq_straight.png ? 250 }}+{{ latex:feynman:lq_single_qll.png ? 250 }}
 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
 +
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(140,100)
 +    \fmfleft{i2,i1}
 +    \fmfright{o2,l2,l1}
 +    % gluon + quarks
 +    \fmf{gluon}{i1,v1}
 +    \fmf{fermion}{i2,v2,o2}
 +    \fmflabel{$g$}{i1}
 +    \fmflabel{$q$}{i2}
 +    \fmflabel{$\ell$}{o2}
 +    % LQs
 +    \fmf{dashes,label=LQ,label.side=left}{v2,v1,LQ}
 +    % LQ -> lepton + quark
 +    \fmf{fermion}{l2,LQ,l1}
 +    \fmflabel{$q$}{l1}
 +    \fmflabel{$\overline{\ell}$}{l2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\
 +{{ latex:feynman:lq_single_qll2_skewed.png ? 250 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,100)
 +    \fmfstraight
 +    \fmfleft{i2,i1}
 +    \fmfright{o2,l2,l1}
 +    % skeleton
 +    \fmf{phantom,tension=1.8}{i1,v1}
 +    \fmf{phantom,tension=1.0}{v1,l1}
 +    \fmf{phantom,tension=1.4}{v1,v2}
 +    \fmf{phantom,tension=1.8}{i2,v2}
 +    \fmf{phantom,tension=1.0}{v2,o2}
 +    \fmffreeze
 +    % gluon + quarks
 +    \fmf{gluon}{i1,v1}
 +    \fmf{fermion}{i2,v2,o2}
 +    \fmflabel{$g$}{i1}
 +    \fmflabel{$q$}{i2}
 +    \fmflabel{$\ell$}{o2}
 +    % LQs
 +    \fmf{dashes,tension=1.2,label=LQ,label.side=left}{v1,LQ}
 +    \fmf{dashes,label=LQ,label.side=left}{v2,v1}
 +    % LQ -> lepton + quark
 +    \fmf{fermion}{l2,LQ,l1}
 +    \fmfshift{5 right}{l1,l2}
 +    \fmfshift{20 left}{o2}
 +    \fmflabel{$q$}{l1}
 +    \fmflabel{$\overline{\ell}$}{l2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\ \\ \\
 +{{ latex:feynman:lq_single_qll2.png ? 250 }}
 +\\ \\ \\ \\ \\
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +% preamble
 +\usepackage{xcolor}
 +\definecolor{myblue}{rgb}{.0,.13,.98} % 0,32,250
 +
 +% body
 +\large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,180)
 +    \fmfleft{i1,iq,i2,ip,i3}
 +    \fmfright{y1,y2,y3,d,o1,o2,f1,o3,f2,d,x3,x2,x1}
 +    \fmfset{arrow_len}{10}
 +    % skeleton
 +    \fmf{phantom,t=0.48}{vq,vp}
 +    \fmf{phantom}{ip,vp,x1}
 +    \fmf{phantom}{iq,vq,y1}
 +    \fmffreeze
 +    \fmf{phantom,t=1.8}{vq,v1,vp}
 +    \fmf{phantom,t=1.8}{v1,v2}
 +    \fmf{phantom,t=1}{o3,v2,o2}
 +    \fmffreeze
 +    % partons
 +    \fmf{fermion,lab=$q$,l.s=right}{vp,v1}
 +    \fmf{gluon,lab=$g$,l.s=left}{vq,v1}
 +    % hard process
 +    \fmf{fermion,lab=$q$,l.s=right}{v1,v2}
 +    \fmf{fermion}{v2,o1}
 +    \fmfshift{10 right}{f1,f2}
 +    \fmf{dashes,t=2,lab=LQ,l.s=left}{v2,vf}
 +    \fmf{phantom,t=0.4}{x1,vf} % pull vf
 +    \fmf{fermion,t=1.4}{f1,vf,f2}
 +    % proton 1
 +    \fmf{phantom}{ip,vp}
 +    \fmfi{fermion}{vpath (__ip,__vp) scaled 1.01 shifted (-2.4, 6)}
 +    \fmfi{fermion}{vpath (__ip,__vp) scaled 1.01 shifted (-2.4, 0)}
 +    \fmfi{fermion}{vpath (__ip,__vp) scaled 1.01 shifted (-2.4,-6)}
 +    % proton 2
 +    \fmf{phantom}{iq,vq}
 +    \fmfi{fermion}{vpath (__iq,__vq) scaled 1.01 shifted (-2.4, 6)}
 +    \fmfi{fermion}{vpath (__iq,__vq) scaled 1.01 shifted (-2.4, 0)}
 +    \fmfi{fermion}{vpath (__iq,__vq) scaled 1.01 shifted (-2.4,-6)}
 +    % X
 +    \fmfshift{25 left}{x1}
 +    \fmfshift{20 left}{x2,x3}
 +    \fmf{phantom}{vp,x1} % to help \fmfi
 +    \fmf{phantom}{vp,x2} % to help \fmfi
 +    \fmf{phantom}{vp,x3} % to help \fmfi
 +    \fmfi{fermion}{vpath (__vp,__x1) scaled 1.0 shifted (0.0, 2.0)}
 +    \fmfi{fermion}{vpath (__vp,__x2) scaled 1.0 shifted (0.0, 0.0)}
 +    \fmfi{fermion}{vpath (__vp,__x3) scaled 1.0 shifted (0.0,-2.0)}
 +    \fmfblob{25}{vp}
 +    % outgoing proton
 +    \fmfshift{25 left}{y1}
 +    \fmfshift{20 left}{y2,y3}
 +    \fmf{phantom}{vq,y1} % to help \fmfi
 +    \fmf{phantom}{vq,y2} % to help \fmfi
 +    \fmf{phantom}{vq,y3} % to help \fmfi
 +    \fmfi{fermion}{vpath (__vq,__y1) scaled 1.0 shifted (0.0,-2.0)}
 +    \fmfi{fermion}{vpath (__vq,__y2) scaled 1.0 shifted (0.0, 0.0)}
 +    \fmfi{fermion}{vpath (__vq,__y3) scaled 1.0 shifted (0.0, 2.0)}
 +    \fmfblob{25}{vq}
 +    % labels
 +    \fmfv{l=$\text{p}^+$,l.a=180,l.d=10}{ip}
 +    \fmfv{l=$\text{p}^+$,l.a=180,l.d=10}{iq}
 +    \fmfv{l=$\overline{\ell}$}{f1}
 +    \fmfv{l=$q$}{f2}
 +    \fmfv{l=$\ell$,l.a=-20}{o1}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=4,f=(.0,,.13,,.98),
 +          l=$\color{myblue}\lambda$,l.d=7,l.a=-10}{v2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\ \\ \\
 +{{ latex:feynman:lq_single_qll_protons.png ? 1000 }}
 +\\ \\ \\ \\ \\
 +</WRAP></WRAP>
 +
 +
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,90)
 +    \fmfstraight
 +    \fmfleft{i2,i1}
 +    \fmfright{o2,l2,l1}
 +    % skeleton
 +    \fmf{phantom,tension=1.8}{i1,v1}
 +    \fmf{phantom,tension=1.1}{v1,l1}
 +    \fmf{phantom,tension=1.6}{v1,v2}
 +    \fmf{phantom,tension=1.8}{i2,v2}
 +    \fmf{phantom,tension=1.1}{v2,o2}
 +    \fmffreeze
 +    % gluon + quarks
 +    \fmf{fermion}{i1,v1}
 +    \fmf{photon}{i2,v2}
 +    \fmf{fermion}{v2,o2}
 +    % LQs
 +    \fmf{dashes,tension=1.2,label=LQ,label.side=left}{v1,LQ}
 +    \fmf{fermion}{v1,v2}
 +    % LQ -> lepton + quark
 +    \fmf{fermion}{l2,LQ,l1}
 +    \fmfshift{5 right}{l1,l2}
 +    \fmfshift{2 down}{l2}
 +    \fmfshift{20 left}{o2}
 +    \fmfv{l.a=160,l=$q$}{i1}
 +    \fmfv{l.a=-165,l=$\gamma$}{i2}
 +    \fmfv{l.a=-20,l=$\ell$}{o2}
 +    \fmfv{l.a=20,l=$\overline{q}$}{l1}
 +    \fmfv{l.a=-10,l=$\overline{\ell}$}{l2}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=4,f=(.0,,.13,,.98),
 +          l=$\color{myblue}\lambda$,l.d=6,l.a=-45}{v1}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\ \\ \\
 +{{ latex:feynman:lq_single_qll_lepton-induced.png ? 250 }}
 +\\ \\ \\ \\ \\
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,190)
 +    \fmfleft{i1,iq,i2,ip,i3}
 +    \fmfright{y1,y2,y3,d,o1,o2,f1,o3,f2,d,x3,x2,x1}
 +    \fmfset{arrow_len}{10}
 +    % skeleton
 +    \fmf{phantom,t=0.48}{vq,vp}
 +    \fmf{phantom,t=1.3}{ip,vp}
 +    \fmf{phantom,t=1.3}{iq,vq}
 +    \fmf{phantom}{vp,x1}
 +    \fmf{phantom}{vq,y1}
 +    \fmffreeze
 +    \fmf{phantom,t=1.6}{vq,v2,v1,vp}
 +    \fmf{phantom,t=0.7}{v1,o3}
 +    \fmf{phantom,t=0.7}{v2,o2}
 +    \fmffreeze
 +    % parton
 +    \fmf{fermion,t=1.6,lab=$q$}{vp,v1}
 +    \fmf{photon,t=1.6,lab=$\gamma$,l.d=3,l.s=left}{vq,v2}
 +    \fmf{fermion,t=1,lab=$\ell$,l.s=right}{v1,v2}
 +    \fmf{fermion,t=1}{v2,o1}
 +    % hard process
 +    \fmfshift{5 right}{f1,f2}
 +    \fmf{dashes,t=2,lab=LQ,l.d=3,l.s=left}{v1,vf}
 +    \fmf{fermion,t=1.4}{f1,vf,f2}
 +    %\fmf{fermion,t=1}{v2,o1}
 +    % proton 1
 +    \fmf{phantom}{ip,vp}
 +    \fmfi{fermion}{vpath (__ip,__vp) scaled 1.01 shifted (-2.4, 6)}
 +    \fmfi{fermion}{vpath (__ip,__vp) scaled 1.01 shifted (-2.4, 0)}
 +    \fmfi{fermion}{vpath (__ip,__vp) scaled 1.01 shifted (-2.4,-6)}
 +    % proton 2
 +    \fmf{phantom}{iq,vq}
 +    \fmfi{fermion}{vpath (__iq,__vq) scaled 1.01 shifted (-2.4, 6)}
 +    \fmfi{fermion}{vpath (__iq,__vq) scaled 1.01 shifted (-2.4, 0)}
 +    \fmfi{fermion}{vpath (__iq,__vq) scaled 1.01 shifted (-2.4,-6)}
 +    % X
 +    \fmfshift{25 left}{x1}
 +    \fmfshift{20 left}{x2,x3}
 +    \fmf{phantom}{vp,x1} % to help \fmfi
 +    \fmf{phantom}{vp,x2} % to help \fmfi
 +    \fmf{phantom}{vp,x3} % to help \fmfi
 +    \fmfi{fermion}{vpath (__vp,__x1) scaled 1.0 shifted ( 0.0, 2.5)}
 +    \fmfi{fermion}{vpath (__vp,__x2) scaled 1.0 shifted ( 0.0, 0.0)}
 +    \fmfi{fermion}{vpath (__vp,__x3) scaled 1.0 shifted ( 0.0,-3.0)}
 +    \fmfblob{22}{vp}
 +    % outgoing proton
 +    \fmfshift{25 left}{y1}
 +    \fmfshift{20 left}{y2,y3}
 +    \fmf{phantom}{vq,y1} % to help \fmfi
 +    \fmf{phantom}{vq,y2} % to help \fmfi
 +    \fmf{phantom}{vq,y3} % to help \fmfi
 +    \fmfi{fermion}{vpath (__vq,__y3) scaled 1.0 shifted (-1.5,-6.0)}
 +    \fmfi{fermion}{vpath (__vq,__y3) scaled 1.0 shifted ( 0.0, 0.0)}
 +    \fmfi{fermion}{vpath (__vq,__y3) scaled 1.0 shifted ( 1.5, 6.0)}
 +    \fmfblob{22}{vq}
 +    % labels
 +    \fmfv{l=$\text{p}^+$,l.a=180,l.d=10}{ip}
 +    \fmfv{l=$\text{p}^+$,l.a=180,l.d=10}{iq}
 +    \fmfv{l=$\text{p}^+$,l.a=-20,l.d=8}{y3}
 +    \fmfv{l=$\overline{\ell}$}{f1}
 +    \fmfv{l=$q$}{f2}
 +    \fmfv{l=$\ell$,l.a=-20}{o1}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=4,f=(.0,,.13,,.98),
 +          l=$\color{myblue}\lambda$,l.d=6,l.a=-45}{v1}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\ \\ \\
 +{{ latex:feynman:lq_single_qll_lepton-induced_protons.png ? 1000 }}
 +\\ \\ \\ \\ \\
 +</WRAP></WRAP>
 +
 +
 + ==== Nonresonant (t-channel) production ====
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(110,60)
 +    \fmfleft{i2,i1}
 +    \fmfright{o2,o1}
 +    \fmf{fermion}{i1,v1,o1}
 +    \fmf{fermion}{o2,v2,i2}
 +    \fmf{dashes,label=LQ,l.s=right,t=0.8}{v1,v2}
 +    \fmfv{l.a=150,l=$q$}{i1}
 +    \fmfv{l.a=30,l=$\ell$}{o1}
 +    \fmfv{l.a=-150,l=$\overline{q}$}{i2}
 +    \fmfv{l.a=-30,l=$\overline{\ell}$}{o2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\
 +{{ latex:feynman:lq_t-channel_ll.png ? 250 }}
 +\\
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,120)
 +    \fmfleft{d,d,g2,d,d,g1,d,d}
 +    \fmfright{b2,d,t2,d,d,t1,d,b1}
 +    % gluons
 +    \fmf{gluon,tension=1.8}{v1,g1}
 +    \fmf{gluon,tension=1.8}{g2,v2}
 +    \fmf{phantom}{v1,t1}
 +    \fmf{phantom}{v2,t2}
 +    \fmffreeze
 +    % b quarks
 +    \fmf{fermion}{b2,v2,vl2}
 +    \fmf{fermion}{vl1,v1,b1}
 +    % LQ (t-channel)
 +    \fmf{dashes,tension=1,label=LQ,l.s=left}{vl1,vl2}
 +    % tau leptons
 +    \fmf{fermion}{t1,vl1}
 +    \fmf{fermion}{vl2,t2}
 +    % labels
 +    \fmfv{l=$g$,l.a=160,l.d=6}{g1}
 +    \fmfv{l=$g$,l.a=-160,l.d=6}{g2}
 +    \fmfv{l=b,l.a=20,l.d=5}{b1}
 +    \fmfv{l=$\overline{\text{b}}$,l.a=-20,l.d=5}{b2}
 +    \fmfv{l=$\tau^+$,l.a=20,l.d=5}{t1}
 +    \fmfv{l=$\tau^-$,l.a=-5,l.d=5}{t2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\
 +{{ latex:feynman:lq_t-channel_bbtautau.png ? 1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 + ===== Z' and W' =====
 +
 +Here are some examples of processes with Z' and W'.
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,60)
 +    \fmfset{arrow_len}{10}
 +    \fmfstraight
 +    \fmfleft{i3,i1}
 +    \fmfright{o3,o2,o1}
 +    % fermions
 +    \fmf{fermion}{i1,v1,o1}
 +    \fmffreeze
 +    \fmf{fermion,tension=1.5}{o3,v3,o2}
 +    \fmf{phantom,tension=1.8}{i3,v3}
 +    \fmflabel{b}{i1}
 +    \fmflabel{c}{o1}
 +    \fmflabel{$\tau$}{o2}
 +    \fmflabel{$\nu_\tau$}{o3}
 +    % boson
 +    \fmf{boson,label=W$'$,label.side=left}{v3,v1}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\
 +{{ latex:feynman:wprime_b_ctaunu.png ? 250 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,60)
 +    \fmfset{arrow_len}{10}
 +    \fmfstraight
 +    \fmfleft{i3,i1}
 +    \fmfright{o3,o2,o1}
 +    % fermions
 +    \fmf{fermion}{i1,v1,o1}
 +    \fmffreeze
 +    \fmf{fermion,tension=1.5}{o3,v3,o2}
 +    \fmf{phantom,tension=1.8}{i3,v3}
 +    \fmflabel{b}{i1}
 +    \fmflabel{s}{o1}
 +    \fmflabel{$\mu$}{o2}
 +    \fmflabel{$\mu$}{o3}
 +    % boson
 +    \fmf{boson,label=Z$'$,label.side=left}{v3,v1}
 +    \fmfblob{16}{v1}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\ \\ \\
 +{{ latex:feynman:zprime_b_smumu.png ? 250 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(110,100)
 +    \fmfleft{i2,i1}
 +    \fmfright{o2,m2,m1,o1}
 +    \fmfshift{30 right}{m1,m2}
 +    \fmf{fermion}{i1,v1,i2}
 +    \fmf{phantom}{o2,v2,o1}
 +    \fmf{boson,label=$\text{Z}/\gamma^*$,label.side=right}{v1,v2}
 +    \fmffreeze
 +    \fmf{fermion}{o2,v2,z,o1}
 +    \fmffreeze
 +    \fmf{boson,label=$\text{Z}'$,label.side=left}{z,m}
 +    \fmf{fermion,tension=1.4}{m2,m,m1}
 +    \fmf{phantom,tension=0.6}{i2,m}
 +    \fmflabel{$\mu^-$}{m1}
 +    \fmflabel{$\mu^+$}{m2}
 +    \fmflabel{$\mu^-$}{o1}
 +    \fmflabel{$\mu^+$}{o2}
 +    \fmflabel{$q$}{i1}
 +    \fmflabel{$\overline{q}'$}{i2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\
 +{{ latex:feynman:zprime_4mu.png ? 450 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +
 +
 +
 + ===== SUSY =====
 +
 +More SUSY diagram are available [[https://twiki.cern.ch/twiki/bin/viewauth/CMS/SUSYSimplifiedModelDiagrams|here (images]] and [[https://github.com/CMS-SUS-XPAG/SUSYDiagrams|here (GitHub)]].
 +
 +<WRAP group><WRAP 55% column lo>
 +<code latex>
 +\large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(80,120)
 +    %\fmfstraight
 +    \fmfleft{i2,b,i1}
 +    \fmfright{o4,o3,o2,o1}
 +    \fmftop{top}
 +    \fmfbottom{bot}
 +    % blob
 +    \fmfblob{16}{b}
 +    \fmf{dashes,tension=1.3,label=$\tilde{\text{t}}$,l.s=right}{v1,b}
 +    \fmf{dashes,tension=1.3,label=$\overline{\tilde{\text{t}}}$,l.s=right}{b,v2}
 +    % decay products
 +    %\fmf{phantom,tension=1.0}{top,v1}
 +    %\fmf{phantom,tension=1.0}{v2,bot}
 +    \fmfshift{16 down}{o1}
 +    \fmfshift{ 8 down}{o2}
 +    \fmfshift{ 8 up}{o3}
 +    \fmfshift{16 up}{o4}
 +    \fmf{dots,tension=1.8}{v1,o1}
 +    \fmf{fermion,tension=1.8}{o2,v1}
 +    \fmf{fermion,tension=1.8}{v2,o4}
 +    \fmf{dots,tension=1.8}{o3,v2}
 +    % labels
 +    \fmflabel{$\tilde{\chi}_1^0$}{o1}
 +    \fmflabel{$\overline{\text{t}}$}{o2}
 +    \fmflabel{$\tilde{\chi}_1^0$}{o3}
 +    \fmflabel{t}{o4}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP 40% column>
 +\\ \\ \\ \\
 +{{ latex:feynman:susy_stop_pair_ttxx.png ? 250 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
  
  
Line 1917: Line 2498:
  ===== Ditau resonance in association with jets =====  ===== Ditau resonance in association with jets =====
  
-Tau pair resonance in association with two quarks, one of which is a b quark, in the t-channel:+Tau pair resonance in association with two quarks, one of which is a b quark, in the t-channel, like single top production:
  
 {{ latex:ditau_jets_t-channel_colored.png ? 400 }} {{ latex:ditau_jets_t-channel_colored.png ? 400 }}
Line 3114: Line 3695:
  
 Here are some proton-proton collisions with hard processes. Note the use of ''\fmfshift'' to shorten the proton debris lines, and make the hard process stick out, without changing the aspect ratio of diagram's other parts. Here are some proton-proton collisions with hard processes. Note the use of ''\fmfshift'' to shorten the proton debris lines, and make the hard process stick out, without changing the aspect ratio of diagram's other parts.
 +
 +Full code for a {{latex:feynman:proton-proton_collisions_hard_process.pdf|multipage PDF}} including all figures below can be found [[latex:feynman:pp_hard|here]].
  
 A generic proces: A generic proces:
Line 3209: Line 3792:
     % hard process     % hard process
     \fmfshift{20 right}{f1,f2}     \fmfshift{20 right}{f1,f2}
-    \fmfv{l=$\bar{f}$}{f1} +    \fmfv{l.a=-25,l.d=3,l=$\ell^+$}{f1} 
-    \fmfv{l=$f$}{f2}+    \fmfv{l.a=25,l.d=5,l=$\ell^-$}{f2}
     \fmf{boson,tension=2,label=$\text{Z}^0/\gamma^*$,label.side=left}{v,vf}     \fmf{boson,tension=2,label=$\text{Z}^0/\gamma^*$,label.side=left}{v,vf}
     \fmf{fermion,tension=2}{f1,vf,f2}     \fmf{fermion,tension=2}{f1,vf,f2}
Line 3252: Line 3835:
 </WRAP><WRAP half column 35%> </WRAP><WRAP half column 35%>
 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
-{{ latex:proton-proton_drell-yan.png ? 0x1000 }}+{{ latex:feynman:proton-proton_drell-yan.png ? 0x1000 }}
 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
Line 3333: Line 3916:
  
 Diffractive processes involving a Pomeron, after [[https://arxiv.org/abs/1208.4968|this ALICE]], [[https://cds.cern.ch/record/2005230?ln=en|this CMS (FSQ-15-005)]] and [[https://cds.cern.ch/record/2194234?ln=en|this ATLAS (ATL-PHYS-PROC-2016-079)]] paper. Note the Pomeron symbol is made with ''${\rm I\!P}$'' instead of ''${\mathbb{P}$''. Diffractive processes involving a Pomeron, after [[https://arxiv.org/abs/1208.4968|this ALICE]], [[https://cds.cern.ch/record/2005230?ln=en|this CMS (FSQ-15-005)]] and [[https://cds.cern.ch/record/2194234?ln=en|this ATLAS (ATL-PHYS-PROC-2016-079)]] paper. Note the Pomeron symbol is made with ''${\rm I\!P}$'' instead of ''${\mathbb{P}$''.
 +
 +Full code for a {{latex:feynman:proton-proton_collisions_diffractive.pdf|multipage PDF}} including all figures below can be found [[latex:feynman:pp_diffractive|here]].
  
 Elastic scattering with Pomeron exchange: Elastic scattering with Pomeron exchange:
Line 3564: Line 4149:
  
  
 + ===== Anomalous momentum measurement (g-2) =====
 +
 +The text colors in the diagrams below are defined with the following in the preamble:
 +<code latex>
 +\usepackage{xcolor}
 +\definecolor{myblue}{rgb}{.1,.1,.7}
 +\definecolor{mygreen}{rgb}{.1,.6,.1}
 +</code>
 +
 +Tree level of photon-tautau vertex:
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\LARGE
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,100)
 +    \fmfbottom{f2,f1}
 +    \fmftop{g}
 +    \fmf{boson,t=1}{g,v}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{f2,v1}
 +    \fmf{plain,f=(.1,,.6,,.1),t=0.9}{v1,v,v2}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{v2,f1}
 +    \fmfv{l.a=-50,l.d=8,l=$\gamma$}{g}
 +    \fmfv{l.a=-25,l=\color{mygreen}$\tau$}{f1}
 +    \fmfv{l.a=-155,l=\color{mygreen}$\tau$}{f2}
 +    \fmffreeze
 +    \fmf{boson,right=0.36,label=$\gamma$,l.s=right}{v1,v2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +{{ latex:feynman:anomalous_momentum_tautau_loop_bent.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +Photon loop:
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\LARGE
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,100)
 +    \fmfbottom{f2,f1}
 +    \fmftop{g}
 +    \fmf{boson,t=1}{g,v}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{f2,v1}
 +    \fmf{plain,f=(.1,,.6,,.1),t=0.9}{v1,v,v2}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{v2,f1}
 +    \fmfv{l.a=-50,l.d=8,l=$\gamma$}{g}
 +    \fmfv{l.a=-25,l=\color{mygreen}$\tau$}{f1}
 +    \fmfv{l.a=-155,l=\color{mygreen}$\tau$}{f2}
 +    \fmffreeze
 +    \fmf{boson,right=0.36,label=$\gamma$,l.s=right}{v1,v2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +{{ latex:feynman:anomalous_momentum_tautau_loop.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +With vacuum polarization quark loop:
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\LARGE
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(160,120)
 +    \fmfbottom{f2,f1}
 +    \fmftop{g}
 +    \fmf{boson,t=1}{g,v}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{f2,v1}
 +    \fmf{fermion,f=(.1,,.6,,.1),t=0.6}{v1,v,v2}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{v2,f1}
 +    \fmfv{l.a=-50,l.d=8,l=$\gamma$}{g}
 +    \fmfv{l.a=-25,l=\color{mygreen}$\tau$}{f1}
 +    \fmfv{l.a=-155,l=\color{mygreen}$\tau$}{f2}
 +    \fmffreeze
 +    \fmf{boson,t=2}{v1,vl1}
 +    \fmf{boson,t=2}{vl2,v2}
 +    \fmf{fermion,left=1,tension=1,label=\Large$q$}{vl1,vl2,vl1}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +{{ latex:feynman:anomalous_momentum_tautau_quarkloop.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +Vertex with blob:
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\LARGE
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,100)
 +    \fmfbottom{f2,f1}
 +    \fmftop{g}
 +    \fmf{boson,t=1.3}{g,v}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{f2,v,f1}
 +    \fmfv{l.a=-25,l=\color{mygreen}$\tau$}{f1}
 +    \fmfv{l.a=-155,l=\color{mygreen}$\tau$}{f2}
 +    \fmfv{decor.shape=circle,decor.filled=shaded,
 +          decor.size=28,f=(.1,,.1,,.7)}{v}
 +    \fmfv{l.a=-50,l.d=8,l=$\gamma$}{g}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +{{ latex:feynman:anomalous_momentum_tautau_blob.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\LARGE
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,100)
 +    \fmfbottom{f2,f1}
 +    \fmftop{g}
 +    \fmf{boson,t=1.3}{g,v}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{f2,v,f1}
 +    \fmfv{l.a=-50,l.d=8,l=$\gamma$}{g}
 +    \fmfv{l.a=-25,l=\color{mygreen}$\tau$}{f1}
 +    \fmfv{l.a=-155,l=\color{mygreen}$\tau$}{f2}
 +    \fmfv{decor.shape=circle,decor.filled=empty,decor.size=35,
 +          f=(.1,,.1,,.7),b=(.92,,.92,,.98),l=\large\color{myblue}$g-2$,l.a=0,l.d=0}{v}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +{{ latex:feynman:anomalous_momentum_tautau_blob_g-2.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\LARGE
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(120,100)
 +    \fmfbottom{f2,f1}
 +    \fmftop{g}
 +    \fmf{boson,t=1}{g,v}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{f2,v1}
 +    \fmf{dashes,left=0.48,t=0.7}{v1,v}
 +    \fmf{dashes,left=0.48,t=0.7,l.d=1pt,label=\Large slepton}{v,v2}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{v2,f1}
 +    \fmf{phantom,t=0.3}{v2,v1}
 +    \fmfv{l.a=-25,l=\color{mygreen}$\tau$}{f1}
 +    \fmfv{l.a=-155,l=\color{mygreen}$\tau$}{f2}
 +    \fmffreeze
 +    \fmf{fermion,l.s=right,l.d=4,l.s=right,
 +         label=\huge$\substack{\text{dark}\\\text{matter}}$}{v1,v2}
 +    \fmfv{l.a=-50,l.d=8,l=$\gamma$}{g}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +{{ latex:feynman:anomalous_momentum_tautau_susy_dm.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +
 +
 + ===== Lepton flavor violating decays =====
 +
 +Some examples of lepton flavor violating (LFV) decays of heavy leptons (muon, tau),
 +which is possible in the Standard Model thanks to neutrino oscillations, but still heavily suppressed due to the small neutrino masses.
 +
 +LVF decay of a heavy leptons (muon, tau) to a lepton plus photon.
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(170,50)
 +    \fmfleft{i1,i2}
 +    \fmfright{o1,o2}
 +    \fmftop{t1,t2}
 +    % fermion lines
 +    \fmf{fermion}{i1,v1} % lepton line in
 +    \fmf{plain,l.d=3,label=$\nu_\ell$\;,t=1.5}{v1,x} % left neutrino line
 +    \fmf{plain,l.d=3,label=\;$\nu_{\ell'}$,t=1.5}{x,v2} % right neutrino line
 +    \fmf{fermion}{v2,o1} % lepton line out
 +    \fmfv{decor.shape=cross,decor.size=10}{x} % cross
 +    \fmffreeze
 +    % loop
 +    \fmf{phantom,t=1}{vl,i2} % support left
 +    \fmf{phantom,t=1.8}{vl,vr} % support middle
 +    \fmf{phantom,t=1}{vr,o2} % support right
 +    \fmf{boson,left=0.25,t=1.2}{v1,vl,vr,v2} % loop
 +    % photon
 +    \fmfshift{30 left}{t2}
 +    \fmf{boson,t=0}{vr,t2} % photon
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=8,l.a=70,l=$\mathrm{W}^-$}{vl}
 +    \fmfv{l.d=5,l.a=15,l=$\gamma$}{t2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_gamma.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +LVF decay of a heavy leptons (muon, tau) to a three leptons, which proceeds through a penguin diagram.
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(140,60)
 +    \fmfstraight
 +    \fmfleft{i1,i2,i3}
 +    \fmfright{o1,o2,o3}
 +    \fmftop{t1,t2}
 +    % fermion lines
 +    \fmf{fermion}{i1,v1} % lepton line in
 +    \fmf{plain,l.d=3,label=$\nu_\ell$\;,t=1.5}{v1,x} % left neutrino line
 +    \fmf{plain,l.d=3,label=\;$\nu_{\ell'}$,t=1.5}{x,v2} % right neutrino line
 +    \fmf{fermion}{v2,o1} % lepton line out
 +    \fmfv{decor.shape=cross,decor.size=10}{x} % cross
 +    \fmffreeze
 +    % loop
 +    \fmf{phantom,t=1.7}{vl,i2} % support left
 +    \fmf{phantom,t=2.4}{vl,vr} % support middle
 +    \fmf{phantom,t=1.7}{vr,o2} % support right
 +    \fmf{boson,left=0.25,t=0.7}{v1,vl,vr,v2} % loop
 +    \fmffreeze
 +    % photon
 +    \fmf{phantom,t=0.9}{t1,vg} % support
 +    \fmfshift{5 right}{o2}
 +    \fmfshift{5 right}{o3}
 +    \fmf{boson,t=1,l.d=4,label=$\gamma$}{vr,vg} % photon
 +    \fmf{fermion,t=1.8}{o3,vg,o2} % fermion
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=5,l.a=-10,l=$\ell'^-$}{o2}
 +    \fmfv{l.d=5,l.a=20,l=$\ell'^+$}{o3}
 +    \fmfv{l.d=8,l.a=70,l=$\mathrm{W}^-$}{vl}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_3lepton.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +LVF decay of a heavy leptons (muon, tau) to a lepton and a photon through a LQ mediator.
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(170,50)
 +    \fmfleft{i1,i2}
 +    \fmfright{o1,o2}
 +    \fmftop{t1,t2}
 +    % fermion lines
 +    \fmf{fermion}{i1,v1} % lepton line in
 +    \fmf{fermion,l.d=6,label=$q$,t=0.75}{v1,v2} % quark line
 +    \fmf{fermion}{v2,o1} % lepton line out
 +    \fmffreeze
 +    % loop
 +    \fmf{phantom,t=1}{vl,i2} % support left
 +    \fmf{phantom,t=1.8}{vl,vr} % support middle
 +    \fmf{phantom,t=1}{vr,o2} % support right
 +    \fmf{boson,left=0.25,t=1.2}{v1,vl,vr,v2} % loop
 +    % photon
 +    \fmfshift{30 left}{t2}
 +    \fmf{boson,t=0}{vr,t2} % photon
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=7,l.a=110,l=LQ}{vl}
 +    \fmfv{l.d=5,l.a=15,l=$\gamma$}{t2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_gamma_lq.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(170,35)
 +    \fmfleft{i1,i2}
 +    \fmfright{o1,o2}
 +    \fmftop{t1,t2}
 +    % fermion lines
 +    \fmf{fermion}{i1,v1} % lepton line in
 +    \fmf{phantom,t=1.2}{v1,v} % support line
 +    \fmf{phantom,t=2.0}{v,v2} % support line
 +    \fmf{fermion}{v2,o1} % lepton line out
 +    \fmffreeze
 +    % internal quark line
 +    \fmf{fermion,l.d=6,l.s=left,label=$q$,t=1}{v1,vm} % quark line
 +    \fmf{plain,t=8}{vm,v2} % quark line
 +    % loop
 +    \fmf{boson,right=0.9,t=1}{v1,v2} % loop
 +    % photon
 +    \fmfshift{30 left}{t2}
 +    \fmf{boson,t=0}{v,t2} % photon
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=22,l.a=-85,l=LQ}{v1}
 +    \fmfv{l.d=5,l.a=15,l=$\gamma$}{t2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_gamma_lq2.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(170,45)
 +    \fmfleft{i1,i2}
 +    \fmfright{o1,o2}
 +    \fmftop{t1,t2}
 +    % fermion lines
 +    \fmf{fermion}{i1,v1} % lepton line in
 +    \fmf{phantom,t=0.85}{v1,v2}
 +    \fmf{fermion}{v2,o1} % lepton line out
 +    \fmffreeze
 +    % loop top
 +    \fmf{phantom,t=1}{vtl,i2} % support left
 +    \fmf{phantom,t=0.6}{vtl,vtr} % support middle
 +    \fmf{phantom,t=1}{vtr,o2} % support right
 +    \fmf{plain,left=0.26,t=1.6}{v1,vtl} % support loop
 +    \fmf{fermion,left=0.26,t=1.6,l.d=5,label=$q$}{vtl,vtr} % fermion loop
 +    \fmf{plain,left=0.26,t=1.6}{vtr,v2} % quark loop
 +    % loop bottom
 +    \fmf{boson,right=1,t=1,label=LQ}{v1,v2} % LQ loop
 +    % photon
 +    \fmfshift{30 left}{t2}
 +    \fmf{boson,t=0}{vtr,t2} % photon
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=5,l.a=20,l=$\gamma$}{t2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_gamma_lq3.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +LVF decay of a heavy leptons (muon, tau) to a three leptons through a LQ mediator.
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(140,60)
 +    \fmfstraight
 +    \fmfleft{i1,i2,i3}
 +    \fmfright{o1,o2,o3}
 +    \fmftop{t1,t2}
 +    % fermion lines
 +    \fmf{fermion}{i1,v1} % lepton line in
 +    \fmf{fermion,l.d=6,label=$q$,t=0.75}{v1,v2} % quark line
 +    \fmf{fermion}{v2,o1} % lepton line out
 +    \fmffreeze
 +    % loop
 +    \fmf{phantom,t=1.7}{vl,i2} % support left
 +    \fmf{phantom,t=2.4}{vl,vr} % support middle
 +    \fmf{phantom,t=1.7}{vr,o2} % support right
 +    \fmf{boson,left=0.25,t=0.7}{v1,vl,vr,v2} % loop
 +    \fmffreeze
 +    % photon
 +    \fmf{phantom,t=0.9}{t1,vg} % support
 +    \fmfshift{5 right}{o2}
 +    \fmfshift{5 right}{o3}
 +    \fmf{boson,t=1,l.d=4,label=$\gamma$}{vr,vg} % photon
 +    \fmf{fermion,t=1.8}{o3,vg,o2} % fermion
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=5,l.a=-10,l=$\ell'^-$}{o2}
 +    \fmfv{l.d=5,l.a=20,l=$\ell'^+$}{o3}
 +    \fmfv{l.d=8,l.a=70,l=LQ}{vl}
 +    %\fmfv{l.d=5,l.a=15,l=$\gamma$}{t2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_3lepton_lq.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(150,50)
 +    \fmfstraight
 +    \fmfleft{i1,i2,i3}
 +    \fmfright{o1,o2,o3}
 +    % fermion lines
 +    \fmf{fermion}{i1,v1} % lepton line in
 +    \fmf{phantom,t=1.2}{v1,v} % support line
 +    \fmf{phantom,t=2.0}{v,v2} % support line
 +    \fmf{fermion}{v2,o1} % lepton line out
 +    \fmffreeze
 +    % internal quark line
 +    \fmf{fermion,l.d=6,l.s=left,label=$q$,t=1}{v1,vm} % quark line
 +    \fmf{plain,t=8}{vm,v2} % quark line
 +    % loop
 +    \fmf{boson,right=0.9,t=1}{v1,v2} % loop
 +    % photon -> 2 leptons
 +    \fmf{boson,t=1,l.d=3,l.s=left,label=$\gamma$}{v,vg} % photon
 +    \fmf{fermion,t=1.6}{o3,vg,o2} % lepton lines
 +    \fmf{phantom,t=1}{i3,vg} % support line
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o2}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^+$}{o3}
 +    \fmfv{l.d=22,l.a=-85,l=LQ}{v1}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_3lepton_lq2.png ? 0x1000 }}
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \large
 +  \begin{fmfgraph*}(130,100)
 +    \fmfleft{i1,i2,i3}
 +    \fmfright{o1,o2,o3}
 +    \fmftop{t1,t2}
 +    \fmfbottom{b1,b2}
 +    % fermion lines
 +    \fmf{fermion}{i2,v1} % lepton line in
 +    \fmf{phantom,t=0.9}{v1,v2}
 +    \fmf{fermion}{v2,o2} % lepton line out
 +    \fmffreeze
 +    % loop top
 +    \fmf{phantom,t=1}{vtl,i3} % support left
 +    \fmf{phantom,t=0.6}{vtl,vtr} % support middle
 +    \fmf{phantom,t=1}{vtr,o3} % support right
 +    \fmf{phantom,left=0.26,t=1.5}{v1,vtl,vtr} % support loop
 +    \fmf{fermion,left=0.26,t=1.5,label=$q$}{vtr,v2} % quark loop
 +    \fmffreeze
 +    \fmf{boson,left=0.57,t=1,l.d=3,label=LQ}{v1,vtr} % LQ loop
 +    % loop bottom
 +    \fmf{phantom,t=1}{vbl,i1} % support left
 +    \fmf{phantom,t=0.6}{vbl,vbr} % support middle
 +    \fmf{phantom,t=1}{vbr,o1} % support right
 +    \fmf{phantom,right=0.26,t=1.5}{v1,vbl,vbr} % support loop
 +    \fmf{boson,right=0.26,t=1.5,l.d=3,label=LQ}{vbr,v2} % LQ loop
 +    \fmffreeze
 +    \fmf{fermion,right=0.57,t=1,label=$q$}{v1,vbr} % quark loop
 +    % fermion
 +    %\fmfshift{10 right}{o1}
 +    %\fmfshift{10 right}{o3}
 +    \fmf{fermion,t=0}{vbr,o1} % fermion
 +    \fmf{fermion,t=0}{o3,vtr} % fermion
 +    % labels
 +    \fmfv{l.d=5,l.a=180,l=$\ell^-$}{i2}
 +    \fmfv{l.d=5,l.a=0,l=$\ell'^-$}{o2}
 +    %\fmfv{l.d=7,l.a=110,l=LQ}{vtl}
 +    \fmfv{l.d=5,l.a=-15,l=$\ell'^-$}{o1}
 +    \fmfv{l.d=5,l.a=20,l=$\ell'^+$}{o3}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\
 +{{ latex:feynman:lfv_lepton_3lepton_lq_loop.png ? 0x1000 }}
 +</WRAP></WRAP>
 + ===== Ultra-peripheral lead-lead collisions =====
 +
 +The text colors in the diagrams below are defined with the following in the preamble:
 +<code latex>
 +\usepackage{xcolor}
 +\definecolor{myblue}{rgb}{.1,.1,.7}
 +\definecolor{myred}{rgb}{.4,.1,.1}
 +\definecolor{mylightred}{rgb}{.9,.1,.1}
 +\definecolor{mygreen}{rgb}{.1,.6,.1}
 +\definecolor{myorange}{rgb}{.9,.7,.2}
 +</code>
 +
 +Measuring the anomalous momentum (g-2) of tau leptons in electron-positron (e+e-) collisions:
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,t2,m,t1,op}
 +    % lead 1
 +    \fmf{fermion}{ip,vp,op}
 +    \fmf{phantom,t=0.3}{ip,vp}
 +    % lead 2
 +    \fmf{fermion}{iq,vq,oq}
 +    \fmf{phantom,t=0.3}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    % mediators
 +    \fmf{phantom,t=0.15}{vt1,im,vt2}
 +    \fmf{phantom,t=0.45}{vt1,vt2}
 +    \fmf{phantom,t=0.5}{vt1,t1}
 +    \fmf{phantom,t=0.5}{vt2,t2}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion,t=4,f=(.1,,.6,,.1)}{vt2,t2}
 +    \fmf{plain,t=1,label=\color{mygreen}$\tau$,l.s=left,f=(.1,,.6,,.1)}{vt2,vt1}
 +    \fmf{fermion,t=4,f=(.1,,.6,,.1)}{vt1,t1}
 +    % labels
 +    \fmfv{l=\strut e$^-$,l.a=160,l.d=4}{ip}
 +    \fmfv{l=\strut e$^-$,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut e$^+$,l.a=-160,l.d=4}{iq}
 +    \fmfv{l=\strut e$^+$,l.a=-20,l.d=5}{oq}
 +    \fmfv{l=\strut\color{mygreen}$\tau^+$,l.a=0,l.d=5}{t1}
 +    \fmfv{l=\strut\color{mygreen}$\tau^-$,l.a=0,l.d=5}{t2}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=4,f=(0.4,,0.1,,0.1)}{vp}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=4,f=(0.4,,0.1,,0.1)}{vq}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4}{vt1}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4}{vt2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:ee_tautau_green.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +
 +Ultra-peripheral lead-lead collisions (UPC) to measure the anomalous momentum (g-2) for tau leptons:
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,t2,m,t1,op}
 +    % lead 1
 +    \fmf{phantom}{ip,vp,op}
 +    \fmf{phantom,t=0.3}{ip,vp}
 +    % lead 2
 +    \fmf{phantom}{iq,vq,oq}
 +    \fmf{phantom,t=0.3}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    % mediators
 +    \fmf{phantom,t=0.15}{vt1,im,vt2}
 +    \fmf{phantom,t=0.45}{vt1,vt2}
 +    \fmf{phantom,t=0.5}{vt1,t1}
 +    \fmf{phantom,t=0.5}{vt2,t2}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmf{double,width=1.9}{ip,vp,op}
 +    \fmf{double,width=1.9}{iq,vq,oq}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion}{vt2,t2}
 +    \fmf{plain,label=$\tau$\!,l.s=left}{vt2,vt1}
 +    \fmf{fermion}{vt1,t1}
 +    % labels
 +    \fmfv{l=\strut Pb,l.a=160,l.d=6}{ip}
 +    \fmfv{l=\strut Pb,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut Pb,l.a=-160,l.d=6}{iq}
 +    \fmfv{l=\strut Pb,l.a=-20,l.d=5}{oq}
 +    \fmfv{l=\strut$\tau^+$,l.a=10,l.d=5}{t1}
 +    \fmfv{l=\strut$\tau^-$,l.a=-10,l.d=5}{t2}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=4}{vt1}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=4}{vt2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:pbpb_tautau.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,t2,m,t1,op}
 +    % lead 1
 +    \fmf{phantom}{ip,vp,op}
 +    \fmf{phantom,t=0.3}{ip,vp}
 +    % lead 2
 +    \fmf{phantom}{iq,vq,oq}
 +    \fmf{phantom,t=0.3}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    \fmfi{double,width=1.9}{vpath (__ip,__vp)}
 +    \fmfi{double,width=1.9}{vpath (__vp,__op)}
 +    \fmfi{double,width=1.9}{vpath (__iq,__vq)}
 +    \fmfi{double,width=1.9}{vpath (__vq,__oq)}
 +    % mediators
 +    \fmf{phantom,t=0.15}{vt1,im,vt2}
 +    \fmf{phantom,t=0.45}{vt1,vt2}
 +    \fmf{phantom,t=0.5}{vt1,t1}
 +    \fmf{phantom,t=0.5}{vt2,t2}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt2,t2}
 +    \fmf{plain,label=\color{mygreen}$\tau$\!,l.s=left,f=(.1,,.6,,.1)}{vt2,vt1}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt1,t1}
 +    % labels
 +    \fmfv{l=\strut Pb,l.a=160,l.d=6}{ip}
 +    \fmfv{l=\strut Pb,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut Pb,l.a=-160,l.d=6}{iq}
 +    \fmfv{l=\strut Pb,l.a=-20,l.d=5}{oq}
 +    \fmfv{l=\strut\color{mygreen}$\tau^+$,l.a=10,l.d=5}{t1}
 +    \fmfv{l=\strut\color{mygreen}$\tau^-$,l.a=-10,l.d=5}{t2}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=90,l.d=8}{vp}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=-90,l.d=8}{vq}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4}{vt1}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4}{vt2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:pbpb_tautau_green.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,t2,m,t1,op}
 +    % lead 1
 +    \fmf{phantom}{ip,vp,op}
 +    \fmf{phantom,t=0.3}{ip,vp}
 +    % lead 2
 +    \fmf{phantom}{iq,vq,oq}
 +    \fmf{phantom,t=0.3}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    \fmfi{double,width=1.9}{vpath (__ip,__vp)}
 +    \fmfi{double,width=1.9}{vpath (__vp,__op)}
 +    \fmfi{double,width=1.9}{vpath (__iq,__vq)}
 +    \fmfi{double,width=1.9}{vpath (__vq,__oq)}
 +    % mediators
 +    \fmf{phantom,t=0.15}{vt1,im,vt2}
 +    \fmf{phantom,t=0.45}{vt1,vt2}
 +    \fmf{phantom,t=0.5}{vt1,t1}
 +    \fmf{phantom,t=0.5}{vt2,t2}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt2,t2}
 +    \fmf{plain,label=\color{mygreen}$\tau$\!,l.s=left,f=(.1,,.6,,.1)}{vt2,vt1}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt1,t1}
 +    % labels
 +    \fmfv{l=\strut Pb,l.a=160,l.d=6}{ip}
 +    \fmfv{l=\strut Pb,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut Pb,l.a=-160,l.d=6}{iq}
 +    \fmfv{l=\strut Pb,l.a=-20,l.d=5}{oq}
 +    \fmfv{l=\strut\color{mygreen}$\tau^+$,l.a=10,l.d=5}{t1}
 +    \fmfv{l=\strut\color{mygreen}$\tau^-$,l.a=-10,l.d=5}{t2}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=90,l.d=8}{vp}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=-90,l.d=8}{vq}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\large$\color{myblue}\delta a_\tau$,l.d=3,l.a=-40}{vt1}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\large$\color{myblue}\delta a_\tau$,l.d=3,l.a=40}{vt2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:pbpb_tautau_green_da.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +With a blob for new physics:
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,t2,m,t1,op}
 +    % proton 1
 +    \fmf{phantom}{ip,vp,op}
 +    \fmf{phantom,t=0.5}{ip,vp}
 +    % proton 2
 +    \fmf{phantom}{iq,vq,oq}
 +    \fmf{phantom,t=0.5}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    \fmfi{double,width=1.9}{vpath (__ip,__vp)}
 +    \fmfi{double,width=1.9}{vpath (__vp,__op)}
 +    \fmfi{double,width=1.9}{vpath (__iq,__vq)}
 +    \fmfi{double,width=1.9}{vpath (__vq,__oq)}
 +    % mediators
 +    \fmf{phantom,t=0.15}{vt1,im,vt2}
 +    \fmf{phantom,t=0.45}{vt1,vt2}
 +    \fmf{phantom,t=0.7}{vt1,t1}
 +    \fmf{phantom,t=0.7}{vt2,t2}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt2,t2}
 +    \fmf{plain,label=\color{mygreen}$\tau$,l.s=left,f=(.1,,.6,,.1)}{vt2,vt1}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt1,t1}
 +    % labels
 +    \fmfv{l=\strut Pb,l.a=160,l.d=6}{ip}
 +    \fmfv{l=\strut Pb,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut Pb,l.a=-160,l.d=6}{iq}
 +    \fmfv{l=\strut Pb,l.a=-20,l.d=5}{oq}
 +    \fmfv{l=\strut\color{mygreen}$\tau^+$,l.a=10,l.d=5}{t1}
 +    \fmfv{l=\strut\color{mygreen}$\tau^-$,l.a=-10,l.d=5}{t2}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=90,l.d=8}{vp}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=-90,l.d=8}{vq}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\;\large$\color{myblue}\delta a_\tau$,l.d=5,l.a=-25}{vt1}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\;\large$\color{myblue}\delta a_\tau$,l.d=5,l.a=25}{vt2}
 +    \fmfblob{18}{vt2,vt1}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:pbpb_tautau_green_blob.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +UPC with neutron emission from electromagnetic dissociation (EMD):
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,d,t2,m,t1,n,op}
 +    \fmfshift{7 right}{op}
 +    \fmfshift{7 right}{oq}
 +    \fmfshift{5 up}{op}
 +    \fmfshift{4 up}{n}
 +    \fmfshift{5 down}{oq}
 +    % lead 1
 +    \fmf{phantom}{ip,vp,op}
 +    \fmf{phantom,t=0.4}{ip,vp}
 +    % lead 2
 +    \fmf{phantom}{iq,vq,oq}
 +    \fmf{phantom,t=0.4}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    \fmf{phantom,label=\:Pb$^*$,l.s=left}{vp,vn} % excited Pb
 +    \fmf{phantom,t=0.9}{vn,op} % relaxed Pb
 +    \fmffreeze
 +    \fmf{phantom,t=0.1}{vn,n} % neutron
 +    \fmffreeze
 +    \fmfi{double,width=1.9}{vpath (__ip,__vp)}
 +    \fmfi{double,width=1.9}{vpath (__vp,__op)}
 +    \fmfi{double,width=1.3}{vpath (__vn,__n)} % neutron
 +    \fmfi{double,width=1.9}{vpath (__iq,__vq)}
 +    \fmfi{double,width=1.9}{vpath (__vq,__oq)}
 +    % mediators
 +    \fmf{phantom,t=0.15}{vt1,im,vt2}
 +    \fmf{phantom,t=0.65}{vt1,vt2} % t-channel
 +    \fmf{phantom,t=0.6}{vt1,t1}
 +    \fmf{phantom,t=0.6}{vt2,t2}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt2,t2}
 +    \fmf{plain,label=\color{mygreen}$\tau$,l.d=4,l.s=left,f=(.1,,.6,,.1)}{vt2,vt1}
 +    \fmf{fermion,f=(.1,,.6,,.1)}{vt1,t1}
 +    % labels
 +    \fmfv{l=n$^0$,l.a=10,l.d=6}{n} % neutron
 +    \fmfv{l=\strut Pb,l.a=160,l.d=6}{ip}
 +    \fmfv{l=\strut Pb,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut Pb,l.a=-160,l.d=6}{iq}
 +    \fmfv{l=\strut Pb,l.a=-20,l.d=5}{oq}
 +    \fmfv{l=\strut\color{mygreen}$\tau^+$,l.a=10,l.d=5}{t1}
 +    \fmfv{l=\strut\color{mygreen}$\tau^-$,l.a=-10,l.d=5}{t2}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$\;\;,l.a=110,l.d=9}{vp}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=-90,l.d=8}{vq}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4}{vt1}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4}{vt2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:pbpb_tautauneutron_green.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +UPC with a pair of tau leptons decaying into a muon and hadrons ("mutau" decay channel):
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,n3,p3,p2,p1,n2,n1,m1,op}
 +    \fmfshift{8 right}{m1}
 +    \fmfshift{8 right}{n1}
 +    \fmfshift{8 right}{n2}
 +    \fmfshift{8 right}{p1}
 +    \fmfshift{8 right}{p2}
 +    \fmfshift{8 right}{p3}
 +    \fmfshift{8 right}{n3}
 +    % proton 1
 +    \fmf{phantom}{ip,vp,op}
 +    \fmf{phantom,t=0.5}{ip,vp}
 +    % proton 2
 +    \fmf{phantom}{iq,vq,oq}
 +    \fmf{phantom,t=0.5}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    \fmfi{double,width=1.9}{vpath (__ip,__vp)}
 +    \fmfi{double,width=1.9}{vpath (__vp,__op)}
 +    \fmfi{double,width=1.9}{vpath (__iq,__vq)}
 +    \fmfi{double,width=1.9}{vpath (__vq,__oq)}
 +    % mediators
 +    \fmf{phantom,t=0.05}{vt1,im,vt2} % pull left
 +    \fmf{phantom,t=0.45}{vt1,vt2} % pull together
 +    \fmf{phantom,t=0.6}{vt1,t1}
 +    \fmf{phantom,t=0.6}{vt2,t2}
 +    \fmf{phantom,t=0.5}{t1,t2} % pull together
 +    \fmf{phantom,t=0.8}{t2,oq} % pull right
 +    \fmf{phantom,t=0.8}{t1,op} % pull right
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion,label=$\tau$,l.s=right}{vt2,t2}
 +    \fmf{plain,label=$\tau$\!,l.s=left}{vt2,vt1}
 +    \fmf{fermion,label=$\tau$,l.s=left}{vt1,t1}
 +    % tau decay 1
 +    \fmf{plain,t=1}{p1,t2}
 +    \fmf{plain,t=1}{t2,p2}
 +    \fmf{plain,t=1}{p3,t2}
 +    \fmf{plain,t=1}{n3,t2}
 +    \fmfv{l=$\pi^\mp$,l.a=0,l.d=5}{p1}
 +    \fmfv{l=$\pi^\pm$,l.a=0,l.d=5}{p2}
 +    \fmfv{l=$\pi^\mp$,l.a=0,l.d=5}{p3}
 +    \fmfv{l=$\overline\nu_\tau$,l.a=-20,l.d=5}{n3}
 +    % tau decay 2
 +    \fmf{plain,t=1}{t1,n1}
 +    \fmf{plain,t=1}{t1,n2}
 +    \fmf{plain,t=1}{t1,m1}
 +    \fmfv{l=$\mu^\pm$,l.a=20,l.d=5}{m1}
 +    \fmfv{l=$\nu_\tau$,l.a=0,l.d=5}{n1}
 +    \fmfv{l=$\nu_\mu$,l.a=0,l.d=5}{n2}
 +    % labels
 +    \fmfv{l=\strut Pb,l.a=160,l.d=6}{ip}
 +    \fmfv{l=\strut Pb,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut Pb,l.a=-160,l.d=6}{iq}
 +    \fmfv{l=\strut Pb,l.a=-20,l.d=5}{oq}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=90,l.d=8}{vp}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=-90,l.d=8}{vq}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\large$\color{myblue}\delta a_\tau$,l.d=3,l.a=-40}{vt1}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\large$\color{myblue}\delta a_\tau$,l.d=3,l.a=40}{vt2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:pbpb_tautau_mutau_3p_blue.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\Large
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(150,100)
 +    \fmfleft{iq,im,ip}
 +    \fmfright{oq,n3,p3,p2,p1,n2,n1,m1,op}
 +    \fmfshift{8 right}{m1}
 +    \fmfshift{8 right}{n1}
 +    \fmfshift{8 right}{n2}
 +    \fmfshift{8 right}{p1}
 +    \fmfshift{8 right}{p2}
 +    \fmfshift{8 right}{p3}
 +    \fmfshift{8 right}{n3}
 +    % proton 1
 +    \fmf{phantom}{ip,vp,op}
 +    \fmf{phantom,t=0.5}{ip,vp}
 +    % proton 2
 +    \fmf{phantom}{iq,vq,oq}
 +    \fmf{phantom,t=0.5}{iq,vq}
 +    \fmf{phantom,t=0.2}{vp,vq}
 +    \fmffreeze
 +    \fmfi{double,width=1.9}{vpath (__ip,__vp)}
 +    \fmfi{double,width=1.9}{vpath (__vp,__op)}
 +    \fmfi{double,width=1.9}{vpath (__iq,__vq)}
 +    \fmfi{double,width=1.9}{vpath (__vq,__oq)}
 +    % mediators
 +    \fmf{phantom,t=0.05}{vt1,im,vt2} % pull left
 +    \fmf{phantom,t=0.45}{vt1,vt2} % pull together
 +    \fmf{phantom,t=0.6}{vt1,t1}
 +    \fmf{phantom,t=0.6}{vt2,t2}
 +    \fmf{phantom,t=0.5}{t1,t2} % pull together
 +    \fmf{phantom,t=0.8}{t2,oq} % pull right
 +    \fmf{phantom,t=0.8}{t1,op} % pull right
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=4,l.s=right}{vp,vt1}
 +    \fmf{boson,t=0.7,label=$\gamma$,l.d=3,l.s=left}{vq,vt2}
 +    \fmffreeze
 +    % taus
 +    \fmf{fermion,label=\color{mygreen}$\tau$,l.s=right,f=(.1,,.6,,.1)}{vt2,t2}
 +    \fmf{plain,label=\color{mygreen}$\tau$\!,l.s=left,f=(.1,,.6,,.1)}{vt2,vt1}
 +    \fmf{fermion,label=\color{mygreen}$\tau$,l.s=left,f=(.1,,.6,,.1)}{vt1,t1}
 +    % tau decay 1
 +    \fmf{plain,t=1,f=(.9,,.7,,.2)}{p1,t2}
 +    \fmf{plain,t=1,f=(.9,,.7,,.2)}{t2,p2}
 +    \fmf{plain,t=1,f=(.9,,.7,,.2)}{p3,t2}
 +    \fmf{plain,t=1,f=(.1,,.6,,.1)}{n3,t2}
 +    \fmfv{l=\color{myorange}$\pi^\mp$,l.a=0,l.d=5}{p1}
 +    \fmfv{l=\color{myorange}$\pi^\pm$,l.a=0,l.d=5}{p2}
 +    \fmfv{l=\color{myorange}$\pi^\mp$,l.a=0,l.d=5}{p3}
 +    \fmfv{l=\color{mygreen}$\overline\nu_\tau$,l.a=-20,l.d=5}{n3}
 +    % tau decay 2
 +    \fmf{plain,t=1,f=(.1,,.6,,.1)}{t1,n1}
 +    \fmf{plain,t=1,f=(.1,,.6,,.1)}{t1,n2}
 +    \fmf{plain,t=1,f=(.9,,.1,,.1)}{t1,m1}
 +    \fmfv{l=\color{mylightred}$\mu^\pm$,l.a=20,l.d=5}{m1}
 +    \fmfv{l=\color{mygreen}$\nu_\tau$,l.a=0,l.d=5}{n1}
 +    \fmfv{l=\color{mygreen}$\nu_\mu$,l.a=0,l.d=5}{n2}
 +    % labels
 +    \fmfv{l=\strut Pb,l.a=160,l.d=6}{ip}
 +    \fmfv{l=\strut Pb,l.a=20,l.d=5}{op}
 +    \fmfv{l=\strut Pb,l.a=-160,l.d=6}{iq}
 +    \fmfv{l=\strut Pb,l.a=-20,l.d=5}{oq}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=90,l.d=8}{vp}
 +    \fmfv{decor.shape=circle,decor.filled=full,decor.size=6,f=(0.4,,0.1,,0.1),
 +          l=$\color{myred}Ze$,l.a=-90,l.d=8}{vq}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\large$\color{myblue}\delta a_\tau$,l.d=3,l.a=-40}{vt1}
 +    \fmfv{decor.shape=circle,f=(0.1,,0.1,,0.7),decor.filled=full,decor.size=4,
 +          l=\large$\color{myblue}\delta a_\tau$,l.d=3,l.a=40}{vt2}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\
 +{{ latex:feynman:pbpb_tautau_mutau_3p_color.png ? 0x1000 }}
 +\\ \\ \\
 +</WRAP></WRAP>
  ===== Penguin diagrams =====  ===== Penguin diagrams =====
  
Line 3597: Line 5154:
 </WRAP><WRAP half column 35%> </WRAP><WRAP half column 35%>
 \\ \\ \\ \\
-{{ latex:penguin_diagram_extra_line.png ? 900 }}+{{ latex:feynman:penguin_diagram_extra_line.png ? 900 }}
 \\ \\ \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
 +
 +
 +<WRAP group><WRAP half column 60% lo>
 +<code latex>
 +\begin{fmffile}{feyngraph}
 +  \begin{fmfgraph*}(140,120)
 +    \fmfstraight
 +    \fmfleft{x,g1,g2,x,s,dsleft,x}
 +    \fmfright{x,n1,n2,x,d,dsright,x}
 +    \fmfbottom{b}
 +    \fmflabel{$\text{b}$}{s}
 +    \fmflabel{$\text{s}$}{d}
 +    \fmf{fermion,tension=1}{dsleft,dsright}
 +    \fmf{fermion,tension=1}{s,v1}
 +    \fmf{fermion,tension=1}{v3,d}
 +    \fmf{photon,label=$\text{W}^-$,label.side=left,tension=1}{v1,v3}
 +    \fmffreeze
 +    \fmf{fermion,label=$\text{t}$,right=0.4,tension=0.2}{v1,v2}
 +    \fmf{fermion,right=0.4,label.side=right,tension=0.2}{v2,v3}
 +    \fmf{phantom,tension=0.20}{v2,b}
 +    \fmffreeze
 +    \fmf{photon,label=$\gamma/\text{Z}^0$,label.side=right,tension=0.5}{v2,v4}
 +    \fmf{fermion,tension=2}{n1,v4,n2}
 +    \fmf{phantom}{g1,v4,g2}
 +    \fmfv{label=$V_\text{ts}^{*}$,label.angle=45,label.dist=3,
 +          %decor.shape=circle, decor.filled=full,decor.size=2thick
 +          }{v3}
 +    \fmfv{label=$V_\text{tb}$,label.angle=120,label.dist=3,
 +          %decor.shape=circle, decor.filled=full,decor.size=2thick
 +          }{v1}
 +    \fmfv{label=$\ell^+$,label.angle=0}{n1}
 +    \fmfv{label=$\ell^-$,label.angle=0}{n2}
 +    \fmfv{label=$\text{$q$}$,label.angle=180}{dsleft}
 +    \fmfv{label=$\text{$q$}$,label.angle=0}{dsright}
 +  \end{fmfgraph*}
 +\end{fmffile}
 +</code>
 +</WRAP><WRAP half column 35%>
 +\\ \\ \\ \\ \\
 +{{ latex:feynman:penguin_diagram_extra_line2.png ? 900 }}
 +\\ \\ \\
 +</WRAP></WRAP>
 +
  
 <WRAP group><WRAP half column 60% lo> <WRAP group><WRAP half column 60% lo>
Line 3617: Line 5217:
 </code> </code>
 </WRAP><WRAP half column 35%> </WRAP><WRAP half column 35%>
-{{ latex:penguin_diagram_triangle.png ? 260 }}+{{ latex:feynman:penguin_diagram_triangle.png ? 260 }}
 </WRAP></WRAP> </WRAP></WRAP>
  
Line 3653: Line 5253:
 </WRAP><WRAP half column 35%> </WRAP><WRAP half column 35%>
 \\ \\ \\ \\
-{{ latex:penguin_diagram_round.png ? 900 }}+{{ latex:feynman:penguin_diagram_round.png ? 900 }}
 \\ \\ \\ \\
 </WRAP></WRAP> </WRAP></WRAP>
latex/feynman.txt · Last modified: 2023/06/06 18:16 by iwn

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